In this tutorial, you will learn how to modify the original 3d topology optimization program (top3d) to solve multiple load cases problem.
In order to solve a multiple load cases problem, as shown below, a few changes need to be made.
Step.1: Define Loading Conditions
First, the loading conditions (line 12) are changed correspondingly:
il = [nelx nelx]; jl = [0 nely]; kl = [nelz/2 nelz/2];
Also the force vector (line 22) and displacement vector (line 23) become more than one column:
F = sparse(loaddof,[1 2],[-1 1],ndof,2); U = zeros(ndof,2);
Step.2: Define Objective Functions
The objective function is now the sum of different load cases
where $M$ is the number of load cases.
Then lines 74-76 are substituted with lines
c = 0.; dc = zeros(nely,nelx,nelz); for i = 1:size(F,2) Ue = U(:,i); ce = reshape(sum((Ue(edofMat)*KE).*Ue(edofMat),2),[nely,nelx,nelz]); c = c + sum(sum(sum((Emin+xPhys.^penal*(E0-Emin)).*ce))); dc = dc - penal*(E0-Emin)*xPhys.^(penal-1).*ce; end
Step.3: Run program
This example is promoted by the line
You will have similar result like this